Show the Proof¶

In [1]:

import proveit
# Automation is not needed when only showing a stored proof:
proveit.defaults.automation = False # This will speed things up.
proveit.defaults.inline_pngs = False # Makes files smaller.
%show_proof

Out[1]:

	step type	requirements	statement
0	modus ponens	1, 2	, , , , , , , , , , ⊢
1	instantiation	3, 69, 4, 5, 58, 71, 6	⊢
	: , : , : , : , : , :
2	instantiation	49, 7, 8	, , , , , , , , , , ⊢
	: , : , :
3	theorem		⊢
	proveit.physics.quantum.algebra.qmult_distribution_over_add
4	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
5	theorem		⊢
	proveit.numbers.numerals.decimals.nat5
6	instantiation	35	⊢
	: , : , : , : , :
7	instantiation	9, 10, 11	, , , , , , , , , , ⊢
	: , :
8	instantiation	56, 12, 13	⊢
	: , : , :
9	theorem		⊢
	proveit.physics.quantum.algebra.qmult_complex_right_closure
10	assumption		⊢
11	instantiation	14, 15	, , , , , , , , , ⊢
	:
12	theorem		⊢
	proveit.numbers.numerals.decimals.posnat7
13	instantiation	16	⊢
	: , : , : , : , : , : , :
14	theorem		⊢
	proveit.physics.quantum.algebra.qmult_nested_closure
15	instantiation	49, 17, 18	, , , , , , , , , ⊢
	: , : , :
16	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_7_typical_eq
17	instantiation	19, 20, 21	, , , , , , , , , ⊢
	: , :
18	instantiation	56, 22, 23	⊢
	: , : , :
19	theorem		⊢
	proveit.physics.quantum.algebra.qmult_complex_left_closure
20	instantiation	49, 24, 25	, , , , , , , , , ⊢
	: , : , :
21	instantiation	26, 76, 77	, ⊢
	: , :
22	theorem		⊢
	proveit.numbers.numerals.decimals.posnat6
23	instantiation	27	⊢
	: , : , : , : , : , :
24	instantiation	28, 29, 66, 30	, , , , , , , , , ⊢
	: , : , :
25	instantiation	56, 31, 32	⊢
	: , : , :
26	theorem		⊢
	proveit.physics.quantum.algebra.qmult_bra_in_QmultCodomain
27	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_6_typical_eq
28	theorem		⊢
	proveit.physics.quantum.algebra.qmult_complex_ket_closure
29	instantiation	49, 33, 34	, , , , , , , , ⊢
	: , : , :
30	assumption		⊢
31	theorem		⊢
	proveit.numbers.numerals.decimals.posnat5
32	instantiation	35	⊢
	: , : , : , : , :
33	instantiation	36, 53, 66, 37, 38	, , , , , , , , ⊢
	: , : , : , :
34	instantiation	56, 39, 40	⊢
	: , : , :
35	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_5_typical_eq
36	theorem		⊢
	proveit.physics.quantum.algebra.qmult_op_ket_is_ket
37	instantiation	59, 53, 66, 41	, , , , , , , ⊢
	: , : , :
38	assumption		⊢
39	theorem		⊢
	proveit.numbers.numerals.decimals.posnat4
40	instantiation	42	⊢
	: , : , : , :
41	instantiation	49, 43, 44	, , , , , , , ⊢
	: , : , :
42	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_4_typical_eq
43	instantiation	64, 45, 53, 66, 46	, , , , , , , ⊢
	: , : , : , :
44	instantiation	56, 69, 47	⊢
	: , : , :
45	assumption		⊢
46	instantiation	59, 53, 66, 48	, , , , , , ⊢
	: , : , :
47	instantiation	80	⊢
	: , : , :
48	instantiation	49, 50, 51	, , , , , , ⊢
	: , : , :
49	theorem		⊢
	proveit.logic.equality.sub_left_side_into
50	instantiation	52, 53, 76, 66, 54, 55	, , , , , , ⊢
	: , : , : , : , :
51	instantiation	56, 57, 58	⊢
	: , : , :
52	theorem		⊢
	proveit.physics.quantum.algebra.qmult_op_op_is_op
53	instantiation	81, 79	⊢
	:
54	instantiation	59, 76, 66, 60	, , ⊢
	: , : , :
55	instantiation	61, 82, 79, 62	, , , , ⊢
	: , : , :
56	axiom		⊢
	proveit.physics.quantum.algebra.multi_qmult_def
57	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
58	instantiation	63	⊢
	: , :
59	theorem		⊢
	proveit.physics.quantum.algebra.qmult_op_is_linmap
60	instantiation	64, 65, 76, 66, 67	, , ⊢
	: , : , : , :
61	theorem		⊢
	proveit.physics.quantum.algebra.qmult_matrix_is_linmap
62	instantiation	68, 69, 70, 71, 72, 73, 74	, , , , ⊢
	: , : , : , :
63	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
64	theorem		⊢
	proveit.physics.quantum.algebra.qmult_op_complex_closure
65	assumption		⊢
66	theorem		⊢
	proveit.linear_algebra.inner_products.complex_set_is_hilbert_space
67	instantiation	75, 76, 77	, ⊢
	: , :
68	theorem		⊢
	proveit.linear_algebra.addition.closure
69	theorem		⊢
	proveit.numbers.numerals.decimals.posnat3
70	instantiation	78, 82, 79	, ⊢
	: , :
71	instantiation	80	⊢
	: , : , :
72	assumption		⊢
73	assumption		⊢
74	assumption		⊢
75	theorem		⊢
	proveit.physics.quantum.algebra.qmult_bra_is_linmap
76	instantiation	81, 82	⊢
	:
77	assumption		⊢
78	theorem		⊢
	proveit.linear_algebra.matrices.complex_matrix_space_is_vec_space
79	assumption		⊢
80	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
81	theorem		⊢
	proveit.linear_algebra.inner_products.complex_vec_set_is_hilbert_space
82	assumption		⊢